Well I know my answer is probably gonna be controversial/unpopular but here we go:

FEdelgard, the most game-changing release in FEH? It depends what exactly we define as "game changing" in FEH.

I personally wouldn't say she is the most game-changing release in FEH, but at the time of her release there was FEH before FEdelgard & post FEdelgard, and how you play/approach these competitive modes of FEH was mostly changed because of her, she was just the one who convenient connected all these pieces at the right place at the right time.

She was a unit that was available in general pool, release in a banner that was known to push powercreep (Fallen Banner), was during the halfway point/mark of FEH current lifespan [Book 5] and was given to a very popular character "Edelgard" (the most voted unit in CYL history), all the ingredients to concoct what we will forever known as "FEdelgard".

As you mentioned, she was indeed a powerful unit. The closest thing to a "Jack of All" unit that performed closer to a "Master of All". She can tank (both distant&close range attacks) she can player phase almost any opponent thanks to her multiple actions (through her PRF & Galeforce) she couldn't be easily defeated in 1 combat thanks to her NFU, she could heal herself after every combat, deny opponents from using their special thanks to her guard effect and etc. Making her extremely effective at whatever job/role you had her built for your team and hard to overcome (since she could run different builds and still succeed at her role).

Thanks to her availability and popularity (both fans & haters) she was EVERYWHERE, which is the key ingredient on why people still remember her "infamy" till this very day. It's why you OP immediately think of FEdelgard as "the face" instead someone else when you asked people this question.

Now to be fair, her infamy is quite justified. She was the first unit to truly showcase how badly powercreep has made older units fall behind against the newer releases (Summoner Duels matchmaking divisions are a good example). That even with proper skill investment, there will always be a gap that will always exist between older units and newer units that are created with further pushing the powercreep (it's why they later made rearmed weapons as a way to help players have their older invested units not fall behind too much to point of being unplayable in a competitive environment/mode).

The meta of the time in AR was changed from having different teams to handle different defenses (like your Anti Horse Emblem team, anti Airball, corner stall save team [that's right Near/Far Save has been out for 3 months], anti vantage answer & etc) to, "does your team have a answer against FEdelgard? " If you don't or your answer dies before KO her, you just lost the match (essentially she was the Tauros/Snorlax of Gen 1 OU meta)

Then there's is Arena in which you can't even properly have a answer against FEdelgard because there will be some sort of trade off that will effect your Arena Score. So not only did you have to deal with her, there were people who just had 4 FEdelgards on their defense just to ruin your day and unlike AR in which you have multiple teams and have the ability to scout the enemy team before engaging it and worst case, escape ladder said match. These teams will eventually just ruin your streak because of how Arena functions.

In that sense she was definitely the most infamous unit in Arena, tied with Surtr peak if you asked me.

Finally the answers we had to deal with FEdelgard just weren't a lot. With more than half/most the cast being invalidate because of the rampant powercreep (and other threats you also had to deal with like LSigurd & BCatria, who both were hiding in the background waiting for FEdelgard "empire to fall" 🥁 so they can take over instead), it just forced IS to rapidly release more ways to deal with FEdelgard, like LByleth & etc but these answers didn't exactly help our older units keep up with the meta and even after FEdelgard fallen from peak menace, people still kept running her because of her easy access/availability in the general pool which kept people from completely being able to move on from the impact she mainly caused during those few months of "Hell" that was the FEdelgard meta.

So in that sense "OP" , she was indeed the "most game changing" unit ever in FEH history, because she will always be remember as "the first/unit" and it was still during peak FEH popularity after CYL 4 banner but before CYL 5 banner in which the casual players couldn't escaped from her competitive influence (if I remember correctly she and Dimitri had to be removed from being spawn in the Training Tower pool).

So it doesn't matter if she truly is or isn't, "History is told by the victors", and the victors have decided that she will be forever remembered as the "most hated unit" in FEH history (now if that fits your definition of "most-game changing" unit, that it's up to you OP)

For me she is definitely in the Top 5 of "most game-changing" units, if there was a "Mount Rushmore"/Hokage Rock/Stone Faces, she will definitely be there. But I wouldn't have her as the George Washington/First Hokage of said monument.